The compact form of the group \(G_2\)  over a real closed field \(k\) 
is the group of automorphisms of the division algebra \(\mathbb {O}\)  of the
octonions. Hence the cohomology set \(H^1(k,G_2(\overline{k}))\)  is
in one-to-one correspondence with the set of \(k\) -isomorphism
classes of \(k\) -algebras which are \(\overline{k}\) -isomorphic to
\(\mathbb {O}\) . In turn, this set is in one-to-one correspondence with the
set of equivalence classes of 3-Pfister forms over \(k\)  (see
[1]} 17.4). A 3-Pfister form over a field \(k\)  is the
quadratic form obtained as the tensor product
\(<1,a>\otimes <1,b> \otimes <1,c>= <1,a,b,ab,c,ac,bc,abc>,\) 
